Solve for $x$ and $y$ using elimination. ${-3x-4y = -22}$ ${3x-5y = -14}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-9y = -36$ $\dfrac{-9y}{{-9}} = \dfrac{-36}{{-9}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-3x-4y = -22}\thinspace$ to find $x$ ${-3x - 4}{(4)}{= -22}$ $-3x-16 = -22$ $-3x-16{+16} = -22{+16}$ $-3x = -6$ $\dfrac{-3x}{{-3}} = \dfrac{-6}{{-3}}$ ${x = 2}$ You can also plug ${y = 4}$ into $\thinspace {3x-5y = -14}\thinspace$ and get the same answer for $x$ : ${3x - 5}{(4)}{= -14}$ ${x = 2}$